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\author{王立庆（2022级数学与应用数学1班）}
\title{数量金融实验 - 第1章课堂练习解答}
%\date{2025年9月9日}

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\begin{document}

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\begin{enumerate}

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\item  %1
有关金融市场，下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  金融市场是资金供应者和资金需求者利用各种金融工具达成交易的场所。
\item[B.]  标的资产包括股票、债券、商品和外汇等。
\item[C.]  标的资产的衍生产品包括远期合约、期货和期权等。
\item[D.]  股票是股份公司资本的构成部分，不可以转让或买卖。
\end{enumerate}

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解答：D. 股票是股份公司资本的构成部分，可以转让、买卖或作价抵押。

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\item  %2
关于金融衍生产品，下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  金融衍生产品是一种风险管理工具。
\item[B.]  金融衍生产品的基本策略是套期保值货称为对冲。
\item[C.]  金融衍生产品是一种合约，合约的买方称为空头，卖方称为多头。
\item[D.]  套期保值是指交易者在现货市场和期货市场对同一类商品进行数量相等但方向相反的买卖活动。
\end{enumerate}

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解答：C. 金融衍生产品是一种合约，合约的买方称为多头，卖方称为空头。

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\item  %3
关于期权，下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  看涨期权是指持有人在未来某个确定时间有权利但不负有义务按确定的价格向期权卖方买入一定数量和质量的标的资产的合约。
\item[B.]  期权是一种未定权益，期权的买方为了获得这种未定权益，必须向期权的卖方支付期权费，也称为期权价格。
\item[C.]  期权的内在价值是指期权的买方在实施期权时可以获得的收益的现值。
\item[D.]  对于看涨期权，当股票价格大于敲定价格时，该期权的内在价值为零。
\end{enumerate}

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解答：D. 对于看涨期权，当股票价格大于敲定价格时，该期权的内在价值大于零。

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\item %4
关于套利和无套利原理，下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  一般地，金融市场是不存在任何套利机会的，这是金融衍生产品定价理论的基石。
\item[B.]  套利是指投资者利用市场价格的差异，在不同市场对某种金融资产同时进行交易，从而获得瞬时无风险收益。
\item[C.]  经济学中的一价定律应用在金融衍生产品定价中，可知所有具有相同收益的投资组合应该具有相同的价格，否则就会产生套利。
\item[D.]  如果一个自融资投资策略 $\Phi$ 存在套利机会，那么一定有 $P(V_0(\Phi)=0)=1$ 和 $P(V_0(\Phi)>0)=1$. 
\end{enumerate}

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解答：D. 一个自融资投资策略 $\Phi$ 称为存在套利机会，是指当 $P(V_0(\Phi)=0)=1$ 时，一定有 $P(V_0(\Phi)\ge 0)=1$ 且 $P(V_0(\Phi)> 0)>0$. 

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\item %5
设在 $t$ 时刻的股票价格为 $S_t$, 无风险利率为 $r$, 设敲定价格为 $X$, 到期日为 $T$. 设不支付红利。关于欧式看涨期权 $c_t$ 和欧式看跌期权 $p_t$, 下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  $c_t$ 和 $p_t$ 满足等式 $c_t + Xe^{-r(T-t)} = p_t +S_t$. 
\item[B.]  看涨期权的价格 $c_t$ 总是低于股票的价格 $S_t$. 
\item[C.]  看涨期权的价格 $c_t$ 总是大于股票的价格减去敲定价格 $S_t-X$. 
\item[D.]  敲定价格越高，欧式看涨期权的价格就越高。
\end{enumerate}

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解答：D. 敲定价格越高，欧式看涨期权的价格就越低。

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\item  %6
假设1年到期的美式看跌期权的敲定价格是100美元，无风险利率是20\%. 如果股票的现价是15美元，那么这份美式看跌期权的持有者提前实施期权，并将收益以20\%的利率存入银行或购买债券，以复利计算，1年后可得收益是多少？
\begin{enumerate}
\item[A.]  103.82.
\item[B.]  104.82.
\item[C.]  105.82.
\item[D.]  106.82.
\end{enumerate}

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解答：A. 提前实施期权，可得收益85美元。复利计算，一年后的收益是 $$85\exp(0.2)=103.82.$$

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\item %7
考虑一个多头欧式看涨期权与空头股票的投资组合，下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  如果股票价格大幅上升，那么投资者在空头股票上遭受损失。
\item[B.]  如果股票价格大幅上升，那么投资者可以实施期权，净亏损为期权费。
\item[C.]  如果股票价格大幅下跌，那么投资者在空头股票上获得利润。
\item[D.]  当股票价格等于敲定价格时，该投资组合的利润为零。
\end{enumerate}

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解答：D. 当股票价格等于敲定价格减去期权费时，该投资组合的利润为零。

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\item %8
投资者预期股票价格在未来12个月内将发生剧烈波动。该股票的现价为100美元。设投资者同时购买一个12月到期的敲定价格都为100美元的欧式看涨期权和欧式看跌期权，组成一个多头跨式期权组合。设这两份期权的价格分别是8美元和7美元。下述说法中，不正确的是哪个？
\begin{enumerate}
\item[A.]  若12个月后股票的价格为70美元，则该投资组合获利15美元。
\item[B.]  若12个月后股票的价格为100美元，则该投资组合损失15美元。
\item[C.]  若12个月后股票的价格为105美元，则该投资组合损失5美元。
\item[D.]  若12个月后股票的价格为130美元，则该投资组合获利15美元。
\end{enumerate}

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解答：C. 若12个月后股票的价格为105美元，则实施看涨期权，获利5美元，扣除两份期权费，净损失10美元。

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\end{enumerate}

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